Browsing Pure Mathematics by Title
Now showing items 43-62 of 165
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The Eberlein Compactification of Locally Compact Groups
(University of Waterloo, 2013-01-24)A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection ... -
Elliptic Curves over Finite Fields and their l-Torsion Galois Representations
(University of Waterloo, 2015-09-08)Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ... -
The Enigma History and Mathematics
(University of Waterloo, 2016-10-25)In this thesis we look at the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, ... -
Equality of Number-Theoretic Functions over Consecutive Integers
(University of Waterloo, 2009-04-30)This thesis will survey a group of problems related to certain number-theoretic functions. In particular, for said functions, these problems take the form of when and how often they are equal over consecutive integers, n ... -
Exact C*-algebras and the Kirchberg-Phillips Nuclear Embedding Theorem
(University of Waterloo, 2019-08-08)A C*-algebra A is exact if the functor A ⊗ min (·) preserves short exact sequences. This is equivalent to the algebra A having a nuclear faithful *-representation. Exact C*-algebras are a class of C*-algebras which is ... -
Exact Formulas for Averages of Secular Coefficients
(University of Waterloo, 2021-09-29)We study averages of secular coefficients that frequently appear in random matrix theory. We obtain exact formulas, identities and new asymptotics for these integrals as well as a technique to deal with singularities that ... -
Exactness and Noncommutative Convexity
(University of Waterloo, 2022-09-02)This thesis studies two separate topics in connection to operator systems theory: the dynamics of locally compact groups, and noncommutative convex geometry. In Chapter 1 we study exactness of locally compact groups as ... -
Existence and uniqueness of weak homotopy moment maps
(Elsevier, 2018-09-01)We show that the classical results on the existence and uniqueness of moment maps in symplectic geometry generalize directly to weak homotopy moment maps in multisymplectic geometry. In particular, we show that their ... -
Exotic Group C*-algebras, Tensor Products, and Related Constructions
(University of Waterloo, 2016-06-15)Recently there has been a rejuvenated interest in exotic group C*-algebras, i.e., group C*-algebras which are "intermediate" to the full and reduced group C*-algebras. This resurgence began with the introduction of the ... -
Families of Thue Inequalities with Transitive Automorphisms
(University of Waterloo, 2014-06-17)A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by ... -
Finitary approximations of free probability, involving combinatorial representation theory
(University of Waterloo, 2023-05-18)This thesis contributes to two theories which approximate free probability by finitary combinatorial structures. The first is finite free probability, which is concerned with expected characteristic polynomials of various ... -
The Fourier algebra of a locally trivial groupoid
(University of Waterloo, 2012-01-10)The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its Fourier-Stieltjes algebra B(G) and its Fourier algebra A(G) were defined by ... -
Free semigroup algebras and the structure of an isometric tuple
(University of Waterloo, 2011-06-28)An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ... -
Generalisations of Roth's theorem on finite abelian groups
(University of Waterloo, 2012-12-18)Roth's theorem, proved by Roth in 1953, states that when A is a subset of the integers [1,N] with A dense enough, A has a three term arithmetic progression (3-AP). Since then the bound originally given by Roth has been ... -
Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations
(University of Waterloo, 2019-07-16)In this thesis we develop generalizations of two well-known principles from the theory of Diophantine approximation, namely the gap principle and the Thue-Siegel principle. Our results find their applications in the theory ... -
Generalized Complex Structures on Kodaira Surfaces
(University of Waterloo, 2014-08-05)In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ... -
Generalized GCDs as Applications of Vojta’s Conjecture
(University of Waterloo, 2023-08-31)Starting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this ... -
Geometrical Frustration and Static Correlations in a Simple Glass Former
(American Physical Society, 2012-01-18)We study the geometrical frustration scenario of glass formation for simple hard-sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding ... -
Geometrical frustration and static correlations in hard-sphere glass formers
(American Institute of Physics, 2013-03-28)We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated ... -
Graph C*-algebras and the Abelian Core
(University of Waterloo, 2016-08-26)We may associate to a C*-algebra to the directed graph E by associating edges to partial isometries and vertices to pairwise orthogonal Hilbert spaces which satisfy some additional conditions. Such graph algebras were first ...